The behavior of a Mode-I interface crack in piezoelectric materials was investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips was negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. It is found that the stress and the electric displacement singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. The solution of the present paper can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.
The behaviors of an interface crack between dissimilar orthotropic elastic halfplanes subjected to uniform tension was reworked by use of the Schmidt method. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, of which the unknown variables are the jumps of the displacements across the crack surfaces. Numerical examples are provided for the stress intensity factors of the cracks. Contrary to the previous solution of the interface crack, it is found that the stress singularity of the present interface crack solution is of the same nature as that for the ordinary crack in homogeneous materials. When the materials from the two half planes are the.same, an exact solution can be otained.
The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack.
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